On the efficiency of path sampling methods for the calculation of free energies from non-equilibrium simulations

Abstract

According to the Jarzynski theorem, equilibrium free energy differences can be calculated from the statistics of work carried out during non-equilibrium transformations. Although exact, this approach can be plagued by large statistical errors, particularly for systems driven strongly away from equilibrium. Recently, several approaches have been suggested to reduce these errors. In this paper we study the efficiency of these methods using two models for which analytical solutions exist.

References in corpus (11)

• A nonequilibrium equality for free energy differences
• An efficient, multiple range random walk algorithm to calculate the density of states
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Rare events and the convergence of exponentially averaged work values
• Theory of Systematic Computational Error in Free Energy Differences
• On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example
• Single-ensemble nonequilibrium path-sampling estimates of free energy differences
• A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution
• Equilibrium free energies from fast-switching trajectories with large time steps

Cited by in corpus (17)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
• Microcanonical quantum fluctuation theorems
• Driving rapidly while remaining in control: classical shortcuts from Hamiltonian to stochastic dynamics
• Asymptotics of work distributions in non-equilibrium systems
• Free energy reconstruction from steered dynamics without post-processing
• On the work distribution in quasi-static processes
• Optimum bias for fast-switching free energy calculations
• Waste-recycling Monte Carlo with optimal estimates: application to free energy calculations in alloys
• Quantum Work Fluctuations in connection with Jarzynski Equality
• Merits and Qualms of Work Fluctuations in Classical Fluctuation Theorems
• Deformed Jarzynski Equality
• Entropy, Free Energy, and Work of Restricted Boltzmann Machines
• Estimation of the equilibrium free energy for glasses using the Jarzynski equality
• Prior-predictive value from fast growth simulations